Characterizing the Rich Variety of Streaming Flow

Steady streaming flow is the result of nonlinear interaction of periodic flow components, used in wide-ranging applications to manipulate positions of particles in microfluidic set-ups. Originating from the oscillatory motion of an interface, the periodic flows can be systematically decomposed e.g. into multipolar components. Self-interaction of modes (inducing single-mode streaming) as well as interaction between distinct modes (inducing mixed-mode streaming) results in qualitatively different spatial patterns of streaming flows, some of which show robust vortex patterns, while others display intricate radial and angular dependencies that can be strongly shifted by even small changes of control parameters such as the relative phases of mixed modes. We demonstrate this rich variety of streaming experimentally using both oscillatory motion over a solid object and oscillatory motion of a fluid-fluid interface. A systematic approach to predicting diverse manifestations of streaming depending on the oscillation modes and boundary conditions is developed, using asymptotic matching in the regime of small streaming Reynolds numbers. The formalism gives indications as to which modes (volumetric, translational, shape) should be combined to obtain a desired streaming pattern for optimal use in particle concentration, separation, or aggregation, and thus provides practical guidelines for device design.